Comparison of effectiveness of multi-objective genetic algorithms in optimization of invertible S-boxes

Strength of modern ciphers depends largely on cryptographic properties of substitution boxes, such as nonlinearity and transparency order. It is difficult to optimize all such properties because they often contradict each other. In this paper we compare two of the most popular multi-objective genetic algorithms, NSGA-II and its steady-state version, in solving the problem of optimizing invertible substitution boxes. In our research we defined objectives as cryptographic properties and observed how they change within population during experiments.